Source code for mxnet.optimizer

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# coding: utf-8
# pylint: disable=too-many-lines
"""Weight updating functions."""
import math
import pickle
import logging
import warnings
import numpy
from .base import py_str
from .ndarray import (NDArray, zeros, clip, sqrt, cast, maximum, abs as NDabs)
from .ndarray import (sgd_update, sgd_mom_update, adam_update, rmsprop_update, rmspropalex_update,
                      mp_sgd_update, mp_sgd_mom_update, square, ftrl_update)
from .ndarray import _internal
from .ndarray import op
from .ndarray import sparse
from .random import normal


[docs]class Optimizer(object): """The base class inherited by all optimizers. Parameters ---------- rescale_grad : float, optional Multiply the gradient with `rescale_grad` before updating. Often choose to be ``1.0/batch_size``. param_idx2name : dict from int to string, optional A dictionary that maps int index to string name. clip_gradient : float, optional Clip the gradient by projecting onto the box ``[-clip_gradient, clip_gradient]``. learning_rate : float, optional The initial learning rate. lr_scheduler : LRScheduler, optional The learning rate scheduler. wd : float, optional The weight decay (or L2 regularization) coefficient. Modifies objective by adding a penalty for having large weights. sym: Symbol, optional The Symbol this optimizer is applying to. begin_num_update : int, optional The initial number of updates. multi_precision : bool, optional Flag to control the internal precision of the optimizer. ``False`` results in using the same precision as the weights (default), ``True`` makes internal 32-bit copy of the weights and applies gradients in 32-bit precision even if actual weights used in the model have lower precision. Turning this on can improve convergence and accuracy when training with float16. Properties ---------- learning_rate: float The current learning rate of the optimizer. Given an Optimizer object optimizer, its learning rate can be accessed as optimizer.learning_rate. """ def __init__(self, rescale_grad=1., param_idx2name=None, wd=0., clip_gradient=None, learning_rate=0.01, lr_scheduler=None, sym=None, begin_num_update=0, multi_precision=False, param_dict=None): self.rescale_grad = rescale_grad self.lr = learning_rate self.lr_scheduler = lr_scheduler if lr_scheduler is not None: self.lr_scheduler.base_lr = learning_rate self.wd = wd self.lr_mult = {} self.wd_mult = {} self.begin_num_update = begin_num_update self.num_update = begin_num_update self._index_update_count = {} self.clip_gradient = clip_gradient self.multi_precision = multi_precision if param_idx2name is None: param_idx2name = {} assert isinstance(param_idx2name, dict), \ 'param_idx2name should be a dict of param indexes to names.' self.idx2name = param_idx2name.copy() self.sym_info = (sym.attr_dict(), sym.list_arguments()) if sym is not None else () self.param_dict = param_dict if param_dict else {} self.set_lr_mult({}) self.set_wd_mult({}) opt_registry = {} @staticmethod
[docs] def register(klass): """Registers a new optimizer. Once an optimizer is registered, we can create an instance of this optimizer with `create_optimizer` later. Examples -------- >>> @mx.optimizer.Optimizer.register ... class MyOptimizer(mx.optimizer.Optimizer): ... pass >>> optim = mx.optimizer.Optimizer.create_optimizer('MyOptimizer') >>> print(type(optim)) """ assert(isinstance(klass, type)) name = klass.__name__.lower() if name in Optimizer.opt_registry: logging.warning('WARNING: New optimizer %s.%s is overriding ' 'existing optimizer %s.%s', klass.__module__, klass.__name__, Optimizer.opt_registry[name].__module__, Optimizer.opt_registry[name].__name__) Optimizer.opt_registry[name] = klass return klass
@staticmethod
[docs] def create_optimizer(name, **kwargs): """Instantiates an optimizer with a given name and kwargs. .. note:: We can use the alias `create` for ``Optimizer.create_optimizer``. Parameters ---------- name: str Name of the optimizer. Should be the name of a subclass of Optimizer. Case insensitive. kwargs: dict Parameters for the optimizer. Returns ------- Optimizer An instantiated optimizer. Examples -------- >>> sgd = mx.optimizer.Optimizer.create_optimizer('sgd') >>> type(sgd) >>> adam = mx.optimizer.create('adam', learning_rate=.1) >>> type(adam) """ if name.lower() in Optimizer.opt_registry: return Optimizer.opt_registry[name.lower()](**kwargs) else: raise ValueError('Cannot find optimizer %s' % name)
@property def learning_rate(self): if self.lr_scheduler is not None: return self.lr_scheduler(self.num_update) else: return self.lr
[docs] def create_state(self, index, weight): """Creates auxiliary state for a given weight. Some optimizers require additional states, e.g. as momentum, in addition to gradients in order to update weights. This function creates state for a given weight which will be used in `update`. This function is called only once for each weight. Parameters ---------- index : int An unique index to identify the weight. weight : NDArray The weight. Returns ------- state : any obj The state associated with the weight. """
[docs] def create_state_multi_precision(self, index, weight): """Creates auxiliary state for a given weight, including FP32 high precision copy if original weight is FP16. This method is provided to perform automatic mixed precision training for optimizers that do not support it themselves. Parameters ---------- index : int An unique index to identify the weight. weight : NDArray The weight. Returns ------- state : any obj The state associated with the weight. """ weight_master_copy = None if self.multi_precision and weight.dtype == numpy.float16: weight_master_copy = weight.astype(numpy.float32) return (weight_master_copy,) + (self.create_state(index, weight_master_copy),) if weight.dtype == numpy.float16 and not self.multi_precision: warnings.warn("Accumulating with float16 in optimizer can lead to " "poor accuracy or slow convergence. " "Consider using multi_precision=True option of the " "optimizer") return self.create_state(index, weight)
[docs] def update(self, index, weight, grad, state): """Updates the given parameter using the corresponding gradient and state. Parameters ---------- index : int The unique index of the parameter into the individual learning rates and weight decays. Learning rates and weight decay may be set via `set_lr_mult()` and `set_wd_mult()`, respectively. weight : NDArray The parameter to be updated. grad : NDArray The gradient of the objective with respect to this parameter. state : any obj The state returned by `create_state()`. """ raise NotImplementedError()
[docs] def update_multi_precision(self, index, weight, grad, state): """Updates the given parameter using the corresponding gradient and state. Mixed precision version. Parameters ---------- index : int The unique index of the parameter into the individual learning rates and weight decays. Learning rates and weight decay may be set via `set_lr_mult()` and `set_wd_mult()`, respectively. weight : NDArray The parameter to be updated. grad : NDArray The gradient of the objective with respect to this parameter. state : any obj The state returned by `create_state()`. """ if self.multi_precision and weight.dtype == numpy.float16: # Wrapper for mixed precision weight_master_copy = state[0] original_state = state[1] grad32 = grad.astype(numpy.float32) self.update(index, weight_master_copy, grad32, original_state) cast(weight_master_copy, dtype=weight.dtype, out=weight) else: self.update(index, weight, grad, state)
[docs] def set_learning_rate(self, lr): """Sets a new learning rate of the optimizer. Parameters ---------- lr : float The new learning rate of the optimizer. """ if self.lr_scheduler is not None: raise UserWarning("LRScheduler of the optimizer has already been " "defined. Note that set_learning_rate can mutate " "the value of the learning rate of the optimizer " "only when the LRScheduler of the optimizer is " "undefined.") else: self.lr = lr
[docs] def set_lr_scale(self, args_lrscale): # pylint: disable=unused-argument """[DEPRECATED] Sets lr scale. Use set_lr_mult instead.""" raise DeprecationWarning
[docs] def set_lr_mult(self, args_lr_mult): """Sets an individual learning rate multiplier for each parameter. If you specify a learning rate multiplier for a parameter, then the learning rate for the parameter will be set as the product of the global learning rate `self.lr` and its multiplier. .. note:: The default learning rate multiplier of a `Variable` can be set with `lr_mult` argument in the constructor. Parameters ---------- args_lr_mult : dict of str/int to float For each of its key-value entries, the learning rate multipler for the parameter specified in the key will be set as the given value. You can specify the parameter with either its name or its index. If you use the name, you should pass `sym` in the constructor, and the name you specified in the key of `args_lr_mult` should match the name of the parameter in `sym`. If you use the index, it should correspond to the index of the parameter used in the `update` method. Specifying a parameter by its index is only supported for backward compatibility, and we recommend to use the name instead. """ self.lr_mult = {} if self.sym_info: attr, arg_names = self.sym_info for name in arg_names: if name in attr and '__lr_mult__' in attr[name]: self.lr_mult[name] = float(attr[name]['__lr_mult__']) self.lr_mult.update(args_lr_mult)
[docs] def set_wd_mult(self, args_wd_mult): """Sets an individual weight decay multiplier for each parameter. By default, if `param_idx2name` was provided in the constructor, the weight decay multipler is set as 0 for all parameters whose name don't end with ``_weight`` or ``_gamma``. .. note:: The default weight decay multiplier for a `Variable` can be set with its `wd_mult` argument in the constructor. Parameters ---------- args_wd_mult : dict of string/int to float For each of its key-value entries, the weight decay multipler for the parameter specified in the key will be set as the given value. You can specify the parameter with either its name or its index. If you use the name, you should pass `sym` in the constructor, and the name you specified in the key of `args_lr_mult` should match the name of the parameter in `sym`. If you use the index, it should correspond to the index of the parameter used in the `update` method. Specifying a parameter by its index is only supported for backward compatibility, and we recommend to use the name instead. """ self.wd_mult = {} for n in self.idx2name.values(): if not (n.endswith('_weight') or n.endswith('_gamma')): self.wd_mult[n] = 0.0 if self.sym_info: attr, arg_names = self.sym_info for name in arg_names: if name in attr and '__wd_mult__' in attr[name]: self.wd_mult[name] = float(attr[name]['__wd_mult__']) self.wd_mult.update(args_wd_mult)
def _update_count(self, index): """Updates num_update. Parameters ---------- index : int The index to be updated. """ if index not in self._index_update_count: self._index_update_count[index] = self.begin_num_update self._index_update_count[index] += 1 self.num_update = max(self._index_update_count[index], self.num_update) def _get_lr(self, index): """Gets the learning rate given the index of the weight. Parameters ---------- index : int The index corresponding to the weight. Returns ------- lr : float Learning rate for this index. """ if self.lr_scheduler is not None: lr = self.lr_scheduler(self.num_update) else: lr = self.lr if index in self.param_dict: lr *= self.param_dict[index].lr_mult elif index in self.lr_mult: lr *= self.lr_mult[index] elif index in self.idx2name: lr *= self.lr_mult.get(self.idx2name[index], 1.0) return lr def _get_wd(self, index): """Gets weight decay for index. Returns 0 for non-weights if the name of weights are provided for `__init__`. Parameters ---------- index : int The index for weight. Returns ------- wd : float Weight decay for this index. """ wd = self.wd if index in self.param_dict: wd *= self.param_dict[index].wd_mult elif index in self.wd_mult: wd *= self.wd_mult[index] elif index in self.idx2name: wd *= self.wd_mult.get(self.idx2name[index], 1.0) return wd
# convenience wrapper for Optimizer.Register register = Optimizer.register # pylint: disable=invalid-name # pylint: disable=line-too-long @register
[docs]class SGD(Optimizer): """The SGD optimizer with momentum and weight decay. The optimizer updates the weight by:: rescaled_grad = lr * rescale_grad * clip(grad, clip_gradient) + wd * weight state = momentum * state + rescaled_grad weight = weight - state If the storage types of weight, state and grad are all ``row_sparse``, \ **sparse updates** are applied by:: for row in grad.indices: rescaled_grad[row] = lr * rescale_grad * clip(grad[row], clip_gradient) + wd * weight[row] state[row] = momentum[row] * state[row] + rescaled_grad[row] weight[row] = weight[row] - state[row] The sparse update only updates the momentum for the weights whose row_sparse gradient indices appear in the current batch, rather than updating it for all indices. Compared with the original update, it can provide large improvements in model training throughput for some applications. However, it provides slightly different semantics than the original update, and may lead to different empirical results. For details of the update algorithm see :class:`~mxnet.ndarray.sgd_update` and :class:`~mxnet.ndarray.sgd_mom_update`. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- momentum : float, optional The momentum value. multi_precision: bool, optional Flag to control the internal precision of the optimizer. ``False`` results in using the same precision as the weights (default), ``True`` makes internal 32-bit copy of the weights and applies gradients \ in 32-bit precision even if actual weights used in the model have lower precision.\ Turning this on can improve convergence and accuracy when training with float16. """ def __init__(self, momentum=0.0, **kwargs): super(SGD, self).__init__(**kwargs) self.momentum = momentum def create_state_multi_precision(self, index, weight): weight_master_copy = None if self.multi_precision and weight.dtype == numpy.float16: weight_master_copy = weight.astype(numpy.float32) return (self.create_state(index, weight_master_copy), weight_master_copy) if weight.dtype == numpy.float16 and not self.multi_precision: warnings.warn("Accumulating with float16 in optimizer can lead to " "poor accuracy or slow convergence. " "Consider using multi_precision=True option of the " "SGD optimizer") return self.create_state(index, weight) def create_state(self, index, weight): momentum = None if self.momentum != 0.0: momentum = zeros(weight.shape, weight.context, dtype=weight.dtype, stype=weight.stype) return momentum def _update_impl(self, index, weight, grad, state, multi_precision=False): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) kwargs = {'rescale_grad': self.rescale_grad} if self.momentum > 0: kwargs['momentum'] = self.momentum if self.clip_gradient: kwargs['clip_gradient'] = self.clip_gradient if not multi_precision: if state is not None: sgd_mom_update(weight, grad, state, out=weight, lr=lr, wd=wd, **kwargs) else: sgd_update(weight, grad, out=weight, lr=lr, wd=wd, **kwargs) else: if state[0] is not None: mp_sgd_mom_update(weight, grad, state[0], state[1], out=weight, lr=lr, wd=wd, **kwargs) else: mp_sgd_update(weight, grad, state[1], out=weight, lr=lr, wd=wd, **kwargs) def update(self, index, weight, grad, state): self._update_impl(index, weight, grad, state, multi_precision=False) def update_multi_precision(self, index, weight, grad, state): use_multi_precision = self.multi_precision and weight.dtype == numpy.float16 self._update_impl(index, weight, grad, state, multi_precision=use_multi_precision)
# pylint: enable=line-too-long @register
[docs]class DCASGD(Optimizer): """The DCASGD optimizer. This class implements the optimizer described in *Asynchronous Stochastic Gradient Descent with Delay Compensation for Distributed Deep Learning*, available at https://arxiv.org/abs/1609.08326. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- momentum : float, optional The momentum value. lamda : float, optional Scale DC value. """ def __init__(self, momentum=0.0, lamda=0.04, **kwargs): super(DCASGD, self).__init__(**kwargs) self.momentum = momentum self.weight_previous = {} self.lamda = lamda def create_state(self, index, weight): if self.momentum == 0.0: return (None, weight.copy()) # previous weight else: return (zeros(weight.shape, weight.context, dtype=weight.dtype), # momentum weight.copy()) # previous weight def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) grad = grad * self.rescale_grad if self.clip_gradient is not None: grad = clip(grad, -self.clip_gradient, self.clip_gradient) mom, previous_weight = state if mom: mom[:] *= self.momentum mom[:] += -lr * (grad + wd * weight + self.lamda \ * grad * grad * (weight - previous_weight)) else: assert(self.momentum == 0.0) mom = -lr * (grad + wd * weight + self.lamda \ * grad * grad * (weight - previous_weight)) previous_weight[:] = weight weight[:] += mom
@register
[docs]class NAG(SGD): """Nesterov accelerated SGD. This optimizer updates each weight by:: state = momentum * state + grad + wd * weight weight = weight - (lr * (grad + momentum * state)) This optimizer accepts the same arguments as :class:`.SGD`. """ def __init__(self, **kwargs): super(NAG, self).__init__(**kwargs) def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) grad = grad * self.rescale_grad if self.clip_gradient is not None: grad = clip(grad, -self.clip_gradient, self.clip_gradient) if state is not None: mom = state mom[:] *= self.momentum grad += wd * weight mom[:] += grad grad[:] += self.momentum * mom weight[:] += -lr * grad else: assert self.momentum == 0.0 weight[:] += -lr * (grad + wd * weight)
@register
[docs]class SGLD(Optimizer): """Stochastic Gradient Riemannian Langevin Dynamics. This class implements the optimizer described in the paper *Stochastic Gradient Riemannian Langevin Dynamics on the Probability Simplex*, available at https://papers.nips.cc/paper/4883-stochastic-gradient-riemannian-langevin-dynamics-on-the-probability-simplex.pdf. """ def __init__(self, **kwargs): super(SGLD, self).__init__(**kwargs) def create_state(self, index, weight): return None def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) grad = grad * self.rescale_grad if self.clip_gradient is not None: grad = clip(grad, -self.clip_gradient, self.clip_gradient) weight[:] += - lr/2 * (grad + wd * weight) + normal(0, math.sqrt(lr), weight.shape, weight.context)
@register # pylint: disable=invalid-name
[docs]class ccSGD(SGD): """[DEPRECATED] Same as `SGD`. Left here for backward compatibility.""" def __init__(self, *args, **kwargs): super(ccSGD, self).__init__(*args, **kwargs)
@register
[docs]class Adam(Optimizer): """The Adam optimizer. This class implements the optimizer described in *Adam: A Method for Stochastic Optimization*, available at http://arxiv.org/abs/1412.6980. The optimizer updates the weight by:: rescaled_grad = clip(grad * rescale_grad + wd * weight, clip_gradient) m = beta1 * m + (1 - beta1) * rescaled_grad v = beta2 * v + (1 - beta2) * (rescaled_grad**2) w = w - learning_rate * m / (sqrt(v) + epsilon) If the storage types of weight, state and grad are all ``row_sparse``, \ **sparse updates** are applied by:: for row in grad.indices: rescaled_grad[row] = clip(grad[row] * rescale_grad + wd * weight[row], clip_gradient) m[row] = beta1 * m[row] + (1 - beta1) * rescaled_grad[row] v[row] = beta2 * v[row] + (1 - beta2) * (rescaled_grad[row]**2) w[row] = w[row] - learning_rate * m[row] / (sqrt(v[row]) + epsilon) The sparse update only updates the mean and var for the weights whose row_sparse gradient indices appear in the current batch, rather than updating it for all indices. Compared with the original update, it can provide large improvements in model training throughput for some applications. However, it provides slightly different semantics than the original update, and may lead to different empirical results. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. For details of the update algorithm, see :class:`~mxnet.ndarray.adam_update`. Parameters ---------- beta1 : float, optional Exponential decay rate for the first moment estimates. beta2 : float, optional Exponential decay rate for the second moment estimates. epsilon : float, optional Small value to avoid division by 0. """ def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8, **kwargs): super(Adam, self).__init__(learning_rate=learning_rate, **kwargs) self.beta1 = beta1 self.beta2 = beta2 self.epsilon = epsilon def create_state(self, index, weight): return (zeros(weight.shape, weight.context, dtype=weight.dtype, stype=weight.stype), # mean zeros(weight.shape, weight.context, dtype=weight.dtype, stype=weight.stype)) # variance def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) t = self._index_update_count[index] coef1 = 1. - self.beta1**t coef2 = 1. - self.beta2**t lr *= math.sqrt(coef2)/coef1 kwargs = {'beta1': self.beta1, 'beta2': self.beta2, 'epsilon': self.epsilon, 'rescale_grad': self.rescale_grad} if self.clip_gradient: kwargs['clip_gradient'] = self.clip_gradient mean, var = state adam_update(weight, grad, mean, var, out=weight, lr=lr, wd=wd, **kwargs)
@register
[docs]class AdaGrad(Optimizer): """AdaGrad optimizer. This class implements the AdaGrad optimizer described in *Adaptive Subgradient Methods for Online Learning and Stochastic Optimization*, and available at http://www.jmlr.org/papers/volume12/duchi11a/duchi11a.pdf. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- eps: float, optional Small value to avoid division by 0. """ def __init__(self, eps=1e-7, **kwargs): super(AdaGrad, self).__init__(**kwargs) self.float_stable_eps = eps def create_state(self, index, weight): return zeros(weight.shape, weight.context, stype=weight.stype) # history def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) is_sparse = True if weight.stype == 'row_sparse' and grad.stype == 'row_sparse' else False if is_sparse is True: grad_indices_count = len(grad.indices) grad = grad * self.rescale_grad if is_sparse is True: grad_indices = grad.indices # Make sure that the scalar multiply still has a sparse result assert grad_indices_count == len(grad_indices) if self.clip_gradient is not None: grad = clip(grad, -self.clip_gradient, self.clip_gradient) history = state save_history_stype = history.stype if is_sparse: history[:] = sparse.elemwise_add(sparse.square(grad), sparse.retain(history, grad_indices)) history_indices = history.indices assert len(history_indices) == grad_indices_count adjusted_add = _internal._scatter_plus_scalar(history, self.float_stable_eps) srt = op.sqrt(adjusted_add) div = _internal._scatter_elemwise_div(grad, srt) retained_weight = sparse.retain(weight, grad.indices) to_add = sparse.elemwise_add(div, _internal._mul_scalar(retained_weight, float(wd))) assert len(to_add.indices) == grad_indices_count weight[:] = sparse.elemwise_add(weight, _internal._mul_scalar(to_add, float(-lr))) state[:] = history assert state.stype == save_history_stype assert len(history_indices) == grad_indices_count else: history[:] += square(grad) div = grad / sqrt(history + self.float_stable_eps) weight[:] += (div + weight * wd) * -lr
@register
[docs]class RMSProp(Optimizer): """The RMSProp optimizer. Two versions of RMSProp are implemented: If ``centered=False``, we follow http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf by Tieleman & Hinton, 2012. For details of the update algorithm see :class:`~mxnet.ndarray.rmsprop_update`. If ``centered=True``, we follow http://arxiv.org/pdf/1308.0850v5.pdf (38)-(45) by Alex Graves, 2013. For details of the update algorithm see :class:`~mxnet.ndarray.rmspropalex_update`. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- gamma1: float, optional A decay factor of moving average over past squared gradient. gamma2: float, optional A "momentum" factor. Only used if `centered`=``True``. epsilon : float, optional Small value to avoid division by 0. centered : bool, optional Flag to control which version of RMSProp to use. ``True`` will use Graves's version of `RMSProp`, ``False`` will use Tieleman & Hinton's version of `RMSProp`. clip_weights : float, optional Clips weights into range ``[-clip_weights, clip_weights]``. """ def __init__(self, learning_rate=0.001, gamma1=0.9, gamma2=0.9, epsilon=1e-8, centered=False, clip_weights=None, **kwargs): super(RMSProp, self).__init__(learning_rate=learning_rate, **kwargs) self.gamma1 = gamma1 self.gamma2 = gamma2 self.centered = centered self.epsilon = epsilon self.clip_weights = clip_weights def create_state(self, index, weight): if self.centered: return ( zeros(weight.shape, weight.context, stype=weight.stype), # n zeros(weight.shape, weight.context, stype=weight.stype), # g zeros(weight.shape, weight.context, stype=weight.stype)) # delta else: return (zeros(weight.shape, weight.context, stype=weight.stype),) # n def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) kwargs = {'gamma1': self.gamma1, 'epsilon': self.epsilon, 'rescale_grad': self.rescale_grad} if self.centered: kwargs['gamma2'] = self.gamma2 if self.clip_gradient: kwargs['clip_gradient'] = self.clip_gradient if self.clip_weights: kwargs['clip_weights'] = self.clip_weights if not self.centered: (n, ) = state rmsprop_update( weight, grad, n, out=weight, lr=lr, wd=wd, **kwargs) else: n, g, delta = state rmspropalex_update(weight, grad, n, g, delta, out=weight, lr=lr, wd=wd, **kwargs)
@register
[docs]class AdaDelta(Optimizer): """The AdaDelta optimizer. This class implements AdaDelta, an optimizer described in *ADADELTA: An adaptive learning rate method*, available at https://arxiv.org/abs/1212.5701. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- rho: float Decay rate for both squared gradients and delta. epsilon : float Small value to avoid division by 0. """ def __init__(self, rho=0.90, epsilon=1e-5, **kwargs): super(AdaDelta, self).__init__(**kwargs) self.rho = rho self.epsilon = epsilon def create_state(self, index, weight): return (zeros(weight.shape, weight.context), # accumulated g zeros(weight.shape, weight.context)) # accumulated delta def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) wd = self._get_wd(index) self._update_count(index) # preprocess grad grad *= self.rescale_grad if self.clip_gradient is not None: grad = clip(grad, -self.clip_gradient, self.clip_gradient) # accumulated g and delta initlization acc_g, acc_delta = state # update g, delta acc_g[:] = self.rho * acc_g + (1. - self.rho) * grad * grad current_delta = sqrt(acc_delta + self.epsilon) / sqrt(acc_g + self.epsilon) * grad acc_delta[:] = self.rho * acc_delta + (1. - self.rho) * current_delta * current_delta # update weight weight[:] -= current_delta + wd * weight
#pylint: disable=invalid-name #pylint: disable=line-too-long @register
[docs]class Ftrl(Optimizer): """The Ftrl optimizer. Referenced from *Ad Click Prediction: a View from the Trenches*, available at http://dl.acm.org/citation.cfm?id=2488200. eta : .. math:: \\eta_{t,i} = \\frac{learningrate}{\\beta+\\sqrt{\\sum_{s=1}^tg_{s,i}^2}} The optimizer updates the weight by:: rescaled_grad = clip(grad * rescale_grad, clip_gradient) z += rescaled_grad - (sqrt(n + rescaled_grad**2) - sqrt(n)) * weight / learning_rate n += rescaled_grad**2 w = (sign(z) * lamda1 - z) / ((beta + sqrt(n)) / learning_rate + wd) * (abs(z) > lamda1) If the storage types of weight, state and grad are all ``row_sparse``, \ **sparse updates** are applied by:: for row in grad.indices: rescaled_grad[row] = clip(grad[row] * rescale_grad, clip_gradient) z[row] += rescaled_grad[row] - (sqrt(n[row] + rescaled_grad[row]**2) - sqrt(n[row])) * weight[row] / learning_rate n[row] += rescaled_grad[row]**2 w[row] = (sign(z[row]) * lamda1 - z[row]) / ((beta + sqrt(n[row])) / learning_rate + wd) * (abs(z[row]) > lamda1) The sparse update only updates the z and n for the weights whose row_sparse gradient indices appear in the current batch, rather than updating it for all indices. Compared with the original update, it can provide large improvements in model training throughput for some applications. However, it provides slightly different semantics than the original update, and may lead to different empirical results. For details of the update algorithm, see :class:`~mxnet.ndarray.ftrl_update`. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- lamda1 : float, optional L1 regularization coefficient. learning_rate : float, optional The initial learning rate. beta : float, optional Per-coordinate learning rate correlation parameter. """ def __init__(self, lamda1=0.01, learning_rate=0.1, beta=1, **kwargs): super(Ftrl, self).__init__(**kwargs) self.lamda1 = lamda1 self.beta = beta self.lr = learning_rate def create_state(self, index, weight): return (zeros(weight.shape, weight.context, stype=weight.stype), # z zeros(weight.shape, weight.context, stype=weight.stype)) # n def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) wd = self._get_wd(index) lr = self._get_lr(index) kwargs = {'lamda1': self.lamda1, 'beta': self.beta, 'rescale_grad': self.rescale_grad} if self.clip_gradient: kwargs['clip_gradient'] = self.clip_gradient # accumulated g and delta initialization z, n = state ftrl_update(weight, grad, z, n, out=weight, lr=lr, wd=wd, **kwargs)
# pylint: enable=line-too-long @register
[docs]class Adamax(Optimizer): """The AdaMax optimizer. It is a variant of Adam based on the infinity norm available at http://arxiv.org/abs/1412.6980 Section 7. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- beta1 : float, optional Exponential decay rate for the first moment estimates. beta2 : float, optional Exponential decay rate for the second moment estimates. """ def __init__(self, learning_rate=0.002, beta1=0.9, beta2=0.999, **kwargs): super(Adamax, self).__init__(learning_rate=learning_rate, **kwargs) self.beta1 = beta1 self.beta2 = beta2 def create_state(self, index, weight): return (zeros(weight.shape, weight.context, dtype=weight.dtype), # mean zeros(weight.shape, weight.context, dtype=weight.dtype)) # variance def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) t = self._index_update_count[index] lr /= (1. - self.beta1**t) # preprocess grad grad = grad * self.rescale_grad + wd * weight if self.clip_gradient is not None: grad = clip(grad, -self.clip_gradient, self.clip_gradient) # update m_t and u_t m_t, u_t = state m_t[:] = self.beta1 * m_t + (1. - self.beta1) * grad u_t[:] = maximum(self.beta2 * u_t, NDabs(grad)) # update weight weight[:] -= lr * m_t / u_t
@register
[docs]class Nadam(Optimizer): """The Nesterov Adam optimizer. Much like Adam is essentially RMSprop with momentum, Nadam is Adam RMSprop with Nesterov momentum available at https://openreview.net/pdf?id=OM0jvwB8jIp57ZJjtNEZ. This optimizer accepts the following parameters in addition to those accepted by :class:`.Optimizer`. Parameters ---------- beta1 : float, optional Exponential decay rate for the first moment estimates. beta2 : float, optional Exponential decay rate for the second moment estimates. epsilon : float, optional Small value to avoid division by 0. schedule_decay : float, optional Exponential decay rate for the momentum schedule """ def __init__(self, learning_rate=0.001, beta1=0.9, beta2=0.999, epsilon=1e-8, schedule_decay=0.004, **kwargs): super(Nadam, self).__init__(learning_rate=learning_rate, **kwargs) self.beta1 = beta1 self.beta2 = beta2 self.epsilon = epsilon self.schedule_decay = schedule_decay self.m_schedule = 1. def create_state(self, index, weight): return (zeros(weight.shape, weight.context, dtype=weight.dtype), # mean zeros(weight.shape, weight.context, dtype=weight.dtype)) # variance def update(self, index, weight, grad, state): assert(isinstance(weight, NDArray)) assert(isinstance(grad, NDArray)) self._update_count(index) lr = self._get_lr(index) wd = self._get_wd(index) t = self._index_update_count[index] # preprocess grad grad *= self.rescale_grad + wd * weight if self.clip_gradient is not None: grad = clip(grad, -self.clip_gradient, self.clip_gradient) # warming momentum schedule momentum_t = self.beta1 * (1. - 0.5 * (pow(0.96, t * self.schedule_decay))) momentum_t_1 = self.beta1 * (1. - 0.5 * (pow(0.96, (t + 1) * self.schedule_decay))) self.m_schedule = self.m_schedule * momentum_t m_schedule_next = self.m_schedule * momentum_t_1 # update m_t and v_t m_t, v_t = state m_t[:] = self.beta1 * m_t + (1. - self.beta1) * grad v_t[:] = self.beta2 * v_t + (1. - self.beta2) * grad * grad grad_prime = grad / (1. - self.m_schedule) m_t_prime = m_t / (1. - m_schedule_next) v_t_prime = v_t / (1. - pow(self.beta2, t)) m_t_bar = (1. - momentum_t) * grad_prime + momentum_t_1 * m_t_prime # update weight weight[:] -= lr * m_t_bar / (sqrt(v_t_prime) + self.epsilon)
@register
[docs]class Test(Optimizer): """The Test optimizer""" def __init__(self, **kwargs): super(Test, self).__init__(**kwargs)
[docs] def create_state(self, index, weight): """Creates a state to duplicate weight.""" return zeros(weight.shape, weight.context)
[docs] def update(self, index, weight, grad, state): """Performs w += rescale_grad * grad.""" weight[:] += grad * self.rescale_grad state[:] = weight
# backward compatibility wrapper for Optimizer.CreateOptimizer create = Optimizer.create_optimizer # pylint: disable=invalid-name
[docs]class Updater(object): """Updater for kvstore.""" def __init__(self, optimizer): self.optimizer = optimizer self.states = {} self.states_synced = {}
[docs] def __call__(self, index, grad, weight): """Updates weight given gradient and index.""" # convert ctypes.char_p.value back to python str if needed if isinstance(index, bytes): index = py_str(index) if index not in self.states: self.states[index] = self.optimizer.create_state_multi_precision(index, weight) self.states_synced[index] = True elif not self.states_synced[index]: self.states[index] = \ self.sync_state_context(self.states[index], weight.context) self.states_synced[index] = True self.optimizer.update_multi_precision(index, weight, grad, self.states[index])
def sync_state_context(self, state, context): if isinstance(state, NDArray): return state.as_in_context(context) elif isinstance(state, (tuple, list)): synced_state = (self.sync_state_context(i, context) for i in state) if isinstance(state, tuple): return tuple(synced_state) else: return list(synced_state) else: return state
[docs] def set_states(self, states): """Sets updater states.""" states = pickle.loads(states) if isinstance(states, tuple) and len(states) == 2: self.states, self.optimizer = states else: self.states = states self.states_synced = dict.fromkeys(self.states.keys(), False)
[docs] def get_states(self, dump_optimizer=False): """Gets updater states. Parameters ---------- dump_optimizer : bool, default False Whether to also save the optimizer itself. This would also save optimizer information such as learning rate and weight decay schedules. """ return pickle.dumps((self.states, self.optimizer) if dump_optimizer else self.states)
[docs]def get_updater(optimizer): """Returns a closure of the updater needed for kvstore. Parameters ---------- optimizer: Optimizer The optimizer. Returns ------- updater: function The closure of the updater. """ return Updater(optimizer)